Systems and methods for pre-averaged staggered convolution decimating filters

ABSTRACT

Certain embodiments of the invention may include systems and methods for implementing a multirate digital decimating filter for filtering received symbol data. The method may include sampling the received symbol data at a selected sample rate, pre-averaging the sampled received data to provide two samples per symbol; convolving the pre-averaged samples with decimated finite impulse response (FIR) aperture impulse response coefficients to produce detected output samples, convolving the pre-averaged samples with shifted decimated FIR aperture impulse response coefficients to produce zero-crossing transition samples, and adjusting the sample rate based at least in part on averaging the zero-crossing transition samples.

FIELD OF THE INVENTION

This invention generally relates to demodulation of signals in variablerate information receiver systems, and in particular, to pre-averagedstaggered convolution decimating filters.

BACKGROUND OF THE INVENTION

Digital data transmission systems have traditionally been designed forspecific applications, and for accommodating relatively narrow ranges ofdata rates. Continuously variable rate transmitter and receiver systems,however, could provide certain desirable flexibilities; for example, inoptimizing variable rate applications for bandwidth requirements, biterror rates, etc. Unfortunately, in order to accommodate flexibleupsampling on the transmitter side, or downsampling on the receiverside, traditional data transmission systems have grown in size andhardware complexity. For example, transmission systems typically requirea linear increase in the number of filter taps, multipliers, adds, anddelay elements for a corresponding increase in the data upsampling anddownsampling rate. Hence, the classical hardware solution may have anorder-of-magnitude growth for each factor-of-ten increase in the samplerate. Another popular alternative to alleviate impractical hardwaregrowth is the repeated use of multiply-accumulate (MAC) functions.However, this technique requires that the MAC run at integer multiplesof the sample rate, greatly restricting top-end speeds. Yet anothertechnique that has been attempted is comb-integrator-comb (CIC)filtering. Unfortunately, CIC filtering is restrictive in terms offilter pass band control characteristics, and CIC register widths tendto grow very large. Furthermore, when CIC filters are used asinterpolators, truncation or rounding errors can produce an unstableresponse.

A need remains for improved systems and methods for downsamplingfilters.

BRIEF SUMMARY OF THE INVENTION

Some or all of the above needs may be addressed by certain embodimentsof the invention. Certain embodiments of the invention may includesystems and methods for providing a pre-averaged staggered convolutiondecimating filter associated with the receiver.

According to an example embodiment of the invention, a method isprovided for implementing a multirate digital decimating filter forfiltering received symbol data. The method includes sampling thereceived symbol data at a selected sample rate, pre-averaging thesampled received data to provide two samples per symbol, convolving thepre-averaged samples with decimated finite impulse response (FIR)aperture impulse response coefficients to produce detected outputsamples, convolving the pre-averaged samples with shifted decimated FIRaperture impulse response coefficients to produce zero-crossingtransition samples, and adjusting the sample rate based at least in parton averaging the zero-crossing transition samples.

According to another example embodiment, a system is provided forimplementing a multirate digital decimating filter for filteringreceived symbol data. The system includes a receiver for receivingsymbol data, at least one memory for storing data andcomputer-executable instructions, at least one processor configured toaccess the at least one memory and further configured to execute thecomputer-executable instructions to: sample the received symbol data ata selected sample rate, pre-average the sampled received data to providetwo samples per symbol, convolve the pre-averaged samples with decimatedFIR aperture impulse response coefficients to produce detected outputsamples, convolve the pre-averaged samples with shifted decimated FIRaperture impulse response coefficients to produce decimated detectedzero-crossing transition samples, and adjust the sample rate based atleast in part on averaging the zero-crossing transition samples.

According to another example embodiment, a filter is provided forfiltering received symbol data. The filter includes at least one memoryfor storing data and computer-executable instructions, at least oneprocessor configured to access the at least one memory and furtherconfigured to execute the computer-executable instructions to: samplethe received symbol data at a selected sample rate, filter the sampledreceived symbol data to remove spectral replicas, pre-average thesampled received data to provide two samples per symbol, convolve thepre-averaged samples with decimated FIR aperture impulse responsecoefficients to produce detected output samples, convolve thepre-averaged samples with shifted decimated FIR aperture impulseresponse coefficients to produce decimated detected zero-crossingtransition samples, and adjust the sample rate based at least in part onaveraging the zero-crossing transition samples.

Other embodiments and aspects of the invention are described in detailherein and are considered a part of the claimed invention. Otherembodiments and aspects can be understood with reference to thefollowing detailed description, and accompanying tables, drawings, andclaims.

BRIEF DESCRIPTION OF THE FIGURES

Reference will now be made to the accompanying figures, which are notnecessarily drawn to scale, and wherein:

FIG. 1 is a block diagram of an illustrative sampling filter accordingto an example embodiment of the invention.

FIG. 2 is a block diagram of an illustrative sampling and filteringsystem according to an example embodiment of the invention.

FIG. 3 is a graphical depiction of a sliding convolution finite impulseresponse (FIR) implementation, according to an example embodiment of theinvention.

FIG. 4 is a block diagram of an illustrative FIR filtering systemaccording to an example embodiment of the invention.

FIG. 5 is a graphical spectral depiction of baseband sampling andreplication removal filtering, according to example embodiments of theinvention.

FIG. 6 is a graphical spectral depiction of intermediate frequency (IF)sampling and replication removal filtering, according to exampleembodiments of the invention.

FIG. 7 is a flow diagram of an example method for implementing amultirate digital interpolating filter, according to an exampleembodiment of the invention.

FIG. 8 is a block diagram of an illustrative decimating filter accordingto an example embodiment of the invention.

FIG. 9 is a block diagram of an illustrative receiver-side sampling andfiltering system according to an example embodiment of the invention.

FIG. 10 is a block diagram of an illustrative pre-averagingfilter/decimator according to an example embodiment of the invention.

FIG. 11 is a graphical depiction of staggered convolution finite impulseresponse (FIR) filtering, according to an example embodiment of theinvention.

FIG. 12 is a graphical depiction of pre-averaging sample decimation,according to example embodiments of the invention.

FIG. 13 is a graphical depiction of an illustrative FIR filtering systemaccording to an example embodiment of the invention.

FIG. 14 is a graphical spectral depiction of anti-aliasing (replicationremoval) with baseband sampling, according to example embodiments of theinvention.

FIG. 15 is a graphical spectral depiction of anti-aliasing (replicationremoval) with IF sampling, according to example embodiments of theinvention.

FIG. 16 is a graphical spectral depiction of pre-averaging frequencyresponse aperture effects for various decimation ratios, according toexample embodiments of the invention.

FIG. 17 is a flow diagram of an example method for implementing amultirate digital decimating filter for filtering received symbol data,according to an example embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention will be described more fully hereinafterwith reference to the accompanying drawings, in which embodiments of theinvention are shown. This invention may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout.

Certain embodiments of the invention may enable variable data ratedigital signal processing (DSP) with fixed hardware implementations.Example embodiments of the invention may provide continuously variablerate (or rate independent) DSP functions that may be associated with adigital communication system. In certain example embodiments of theinvention, systems and methods are provided to implement variable ratedigital data interpolation functions that may typically be associatedwith the transmitter side of a communications system. In other exampleembodiments of the invention, systems and methods are provided toimplement variable rate decimation functions that may typically beassociated with the receiver side of a communications system. Accordingto example embodiments of the invention, signal processing may includevarious combinations of sampling, filtering, convolving, etc., forbandlimiting digital signals, and for removing replication spectra thatresult from digital sampling.

Example embodiments of the invention, including a sliding convolutioninterpolating (SCI) filter and a pre-averaged staggered convolutiondecimating (PASCoDec) filter, will now be described with reference tothe accompanying figures.

Sliding Convolution Interpolating (SCI) Filter

According to example embodiments of the invention, a sliding convolutioninterpolating (SCI) filter is provided. The name “multirate digitalinterpolating filter” may be used interchangeably to denote the SCIfilter. There are countless generic, digital signal processing (DSP)interpolation situations to which the SCI filter could apply. One aspectof the invention, which will become apparent as further details arepresented, is the relatively rate-independent interpolation functionthat can be implemented without requiring corresponding changes in DSPhardware to accommodate different data rates. For example, the DSPhardware may be fixed, and the speed flexibility may be achieved byburdening memory whose densities and speeds are typically doubling everytwo years, in accordance with the well-known Moore's law.

An example application for the SCI filter is a Nyquist bandlimitingfilter in a digital data transmission system. In accordance with exampleembodiments of the invention, the SCI filter may make repeated use of asliding convolution function, where a reduced set of staggeredcoefficients are successively applied to a relatively compact,finite-impulse-response (FIR) circuit topology. In this manner, thenumber of digital multipliers and adds (e.g., hardware) required for theFIR remains fixed, while the memory size would grow with the number ofsamples per symbol needed. According to example embodiments of theinvention, continuously variable data rate operation is achievable withthis sample interpolation scheme, by increasing the number of samplesper symbol as the data rate is reduced.

An example Nyquist bandlimiting interpolating system 100 is shown inFIG. 1. According to example embodiments, an interpolating spectralshaping filter 102 may apply the FIR coefficients 104 to the inputdigital data 106 to produce Nyquist-shaped samples 112, which may beinterpolated bandlimited data at N samples/symbol. Therefore, inaccordance with example embodiments of the invention, the input digitaldata 106 may be sampled and upconverted from 1 sample/symbol to Nsamples per symbol, where the upconversion ratio may be set by thesample rate input Rs 108 and the upconversion rate input NRs 110.

FIG. 2 depicts a block diagram of an example Nyquist bandlimitinginterpolation system 200. According to example embodiments of theinvention, certain hardware may be included for implementing the Nyquistbandlimiting system. For example, the system 200 may include one or moreprocessors 202 and one or more memories 204 accessible by the one ormore processors 202. Filter coefficients 206 may be stored in the one ormore memories 204, and may be utilized in a convolution with digitaldata in 218 via a FIR filter 208. The FIR filter may include shiftregisters 210, multipliers 214, and summing nodes 216. The FIR filter208 may produce output bandlimited N-interpolated data 220, which may bemodulated or upconverted by an optional modulator 222, for example, tothe produce radio frequency (RF) output 224. According to exampleembodiments, the one or more processors 202 may be configured,programmed, or operable to perform memory accesses, timing, and otherfunctions associated with the convolution process. A particularimplementation of the Nyquist bandlimiting interpolation system 200 willbe discussed below with reference to FIGS. 3 and 4.

FIG. 3 is a graphical representation of upsampling and bandlimitfiltering 300, according to example embodiments of the invention. Shownin FIG. 3 is a periodic, binary sample stream 304 representing thedigital data input that may be continuously clocked 303 into theinterpolating spectral shaping filter 102 at one sample per symbol. Theperiodic, binary sample stream 304 may be convolved with one set(darkened samples) from each of the FIR filter waveform samples 306, andalso with the filter waveform samples (308, 310, 312) staggered by 1 toN samples to produce the output interpolated bandlimited data 314. Inother words, each sample in the periodic, binary sample stream 304 maybe convolved with sets of FIR filter coefficients (decimated FIRaperture impulse response coefficient set and shifted decimated FIRaperture impulse response coefficient sets) 316 at one sample per symbolyielding a single output value per sample for each convolution. Inexample embodiments of the invention the FIR filter waveformcoefficients may be selected from any number of FIR filter impulseresponses. In an example embodiment, the FIR filter waveform samples(e.g., the decimated FIR aperture impulse response coefficient sets 316)may be modeled from a “raised cosine” impulse response, which is awell-known filtering function of the Nyquist filter family. Next,staggered filter waveform samples (308, 310, 312) are repeatedlyconvolved against the same input samples 304, effectively providingfiltering at the output upsample rate, N samples per symbol. Thesummation of each sparsely populated impulse response (306, 308, 310,312), convolved with the input sequence (304) produces the periodicallyspaced output samples (output interpolated bandlimited data) 314.Therefore, the sample values in the gaps of the periodic, binary samplestream 304 are interpolated through these repeated convolutions with thestaggered impulse responses. In this manner, upsampling, interpolation,spectral shaping, and pre-distortion, if desired, are all achieved in asingle FIR processing block.

According to an example embodiment of the invention, a generalized blockdiagram of an interpolating FIR circuit topology 400 is shown in FIG. 4.In this example embodiment, a FIR coefficient memory 401 may be utilizedto store and access FIR coefficients. The topology 400 may include aplurality of shift registers 404, multipliers 412, and summation blocks414. In an example embodiment, an input sample stream 402, which maycomprise periodic binary samples, may be continuously clocked throughthe shift registers 404. Then, after each shifting, the sample 408 atthe input and the successively shifted samples 406 may be multiplied viamultipliers 412 with FIR coefficients 410. The resulting samples maythen be successively summed by summing nodes 414, resulting in outputfiltered bandlimited data 416.

Example values for the various elements of the interpolating FIR circuittopology 400 may include: aperture widths=eight symbol times (depictedby the number of shift registers T 404); 8×8-bit digital multipliers412; data symbol rate range operable to vary over threeorders-of-magnitude; data sample rate range about half an octave; andFIR coefficient memory 401 size approximately equal to the maximumnumber of samples per symbol times number of symbols in aperture timesthe number of bits per sample. Hence, as is apparent from FIG. 4, theperformance burden is on the memory size and speed to keep theimplementation compact.

TABLE 1 below lists sample rates and ranges for continuously variablerate operation with baseband gear shifting for a sliding convolutioninterpolating filter, according to an example embodiment of theinvention. Continuously variable rate operation may be achieved by gearshifting the number of samples per symbol. In this manner, the samplerate may be kept in a fixed range, such that only a single replicationremoval (RR) filter is necessary. In TABLE 1, a maximum data rate of 60M symbols/sec has been arbitrarily set for illustration purposes. Notethat each octave in the data symbol rate is broken up into two ratioregions, 1:1.5 and 1:1.33; where the upper range always has samples persymbol that are powers-of-two, and the lower range has samples persymbol that are powers-of-two times three. Also, observe that the samplerates always fall within a 1:1.5 range. Hence, in a motor vehicleanalogy, the sample rate is analogous to engine RPM, the number ofsamples per symbol to the gear ratio, and the data symbol rate to actualvehicle speed. The lowest integer power would be two samples per symbol,for this type of application using baseband Nyquist sampling.

TABLE 1 Baseband Sample Rates Symbol Rate Range Samples/ Sample RateRange Min (Ksps) Max (Ksps) Symbol Min (Msps) Max (Msps) 58.59 78.131536 90.00 120.00 78.13 117.19 1024 80.00 120.00 117.19 156.25 768 90.00120.00 156.25 234.38 512 80.00 120.00 234.38 312.50 384 90.00 120.00312.50 468.75 256 80.00 120.00 468.75 625.00 192 90.00 120.00 625.00937.50 128 80.00 120.00 937.50 1250.00 96 90.00 120.00 1250.00 1875.0064 80.00 120.00 1875.00 2500.00 48 90.00 120.00 2500.00 3750.00 32 80.00120.00 3750.00 5000.00 24 90.00 120.00 5000.00 7500.00 16 80.00 120.007500.00 10000.00 12 90.00 120.00 10000.00 15000.00 8 80.00 120.0015000.00 20000.00 6 90.00 120.00 20000.00 30000.00 4 80.00 120.0030000.00 40000.00 3 90.00 120.00 40000.00 60000.00 2 80.00 120.00

The gear-shifting technique 500 is depicted in the frequency-domain forbaseband sampling in FIG. 5. In this figure, a replication removal (RR)filter 520 is situated to remove all sampling rate replicas 516 (but topass the baseband spectra 514) for the case where the data rate iscontinuously varied. Typically an elliptic analog filter function wouldbe used as the RR filter 520 with an equiripple bandwidth on the orderof ¾ the maximum data symbol rate, with a passband-to-stopbandshapefactor on the order of 1:1.5. FIG. 5 shows the spectral filteringconditions at the minimum 508 and maximum 506 rates for two samples persymbol in the highest octave of operation. Also shown are spectralfiltering conditions at the minimum 512 and maximum 510 rates for threesamples per symbol in the highest octave of operation. Subsequentoctaves occupy less bandwidth and are progressively less affected by theRR filter characteristics. Also depicted in FIG. 5 is a point near thecentral part of the replicas representing a zero crossing 518. This zerocrossing occurs at the 2f/R frequency and is due to a sinc(=sin(πf/R)/(πf/R)) shape zero crossing that arises because the inputsamples are actually sampled and held, resulting in a sinc spectrum.

TABLE 2 below lists sample rates and ranges for continuously variablerate operation with intermediate frequency (IF) gear shifting for asliding convolution interpolating filter, according to an exampleembodiment of the invention. TABLE 2 differs from TABLE 1 in that theminimum number of samples per symbol for IF sampling is double what itis for baseband sampling. Hence, the maximum data rate is halved. Thisdoubling is a direct result of it being more difficult to avoid aliasingwith IF sampling. Continuously variable rate operation is stillachievable, but for a given hardware technology, the maximum data rateof operation is halved. IF sampling has other advantages in that it usesless hardware than baseband sampling, and the quadrature amplitude andphase balance is automatic and precise.

TABLE 2 IF Sample Rates Symbol Rate Range Samples/ Sample Rate Range Min(Ksps) Max (Ksps) Symbol Min (Msps) Max (Msps) 29.30 39.06 3072 90.00120.00 39.06 58.59 2048 80.00 120.00 58.59 78.13 1536 90.00 120.00 78.13117.19 1024 80.00 120.00 117.19 156.25 768 90.00 120.00 156.25 234.38512 80.00 120.00 234.38 312.50 384 90.00 120.00 312.50 468.75 256 80.00120.00 468.75 625.00 192 90.00 120.00 625.00 937.50 128 80.00 120.00937.50 1250.00 96 90.00 120.00 1250.00 1875.00 64 80.00 120.00 1875.002500.00 48 90.00 120.00 2500.00 3750.00 32 80.00 120.00 3750.00 5000.0024 90.00 120.00 5000.00 7500.00 16 80.00 120.00 7500.00 10000.00 1290.00 120.00 10000.00 15000.00 8 80.00 120.00 15000.00 20000.00 6 90.00120.00 20000.00 30000.00 4 80.00 120.00

In FIG. 6, gear shifting is graphically depicted for the case of IFsampling in the first Nyquist zone, where f_(if)/R_(sym)=1. Areplication removal (RR) filter 620 is situated to remove all samplingrate replicas 616, 618 (but to pass the first IF spectra 614). Typicallyan elliptic analog filter function would be used as the RR filter 620with an equiripple bandwidth on the order of 3/2 the maximum data symbolrate, with a passband-to-stopband shapefactor on the order of 1:1.5.FIG. 6 shows the spectral filtering conditions at the minimum 608 andmaximum 606 rates for four samples per symbol in the highest octave ofoperation. Also shown are spectral filtering conditions at the minimum612 and maximum 610 rates for six samples per symbol in the highestoctave of operation. Subsequent octaves occupy less bandwidth and areprogressively less affected by the RR filter characteristics

In this spectral depiction, the continuously variable rate operation isanalogous to the baseband case shown in FIG. 5. The spectral occupancyat the highest data rate in the first octave of operation is so broadthat the same low pass elliptic RR filter is applicable. An aspect ofthis implementation is that it can be largely digitally switched fromlow pass to band pass sampling, without changing the RR filter.

An example method 700 for implementing a multirate digital interpolatingfilter (e.g., a sliding convolution interpolating SCI filter) will nowbe described with reference to the flow diagram of FIG. 7. In block 702and according to an example embodiment of the invention, the method mayinclude sampling symbol data from one sample per symbol to N samples persymbol. In block 704, the sampled symbol data may be convolved with adecimated FIR aperture impulse response coefficient set. In block 706,the symbol data may be convolved with one or more shifted decimated FIRaperture impulse response sets. In block 708, the convolution resultsmay be summed to produce interpolated bandlimited data.

Additional aspects or embodiments of the invention may include systemsand methods that may enable sampling the symbol data, where samplingcomprises one or more of upsampling or spectral-shaping symbol data.According to example embodiments, convolving the symbol data withshifted decimated FIR aperture impulse response coefficient setscomprises convolving the symbol data with one-to-N-shifted decimated FIRaperture impulse response coefficient sets, wherein the one-to-N-shifteddecimated FIR aperture impulse response coefficient sets are shifted byone-to-N samples with respect to the decimated FIR aperture impulseresponse coefficient sets. Embodiments of the invention may also includefiltering the interpolated bandlimited data to remove spectral replicas.

According to example embodiments of the invention, sampling the symboldata may comprise sampling digital symbols, wherein the digital symbolscomprise one or more of in-phase or quadrature-phase symbol data.Furthermore, convolving the symbol data with the decimated FIR apertureimpulse response coefficient set may comprise convolving the symbol datawith a Nyquist filtering function. According to example embodiments ofthe invention, sampling symbol data provides a sample per symbol rate ofpowers-of-two times three or powers-of-two.

The sliding convolution interpolating (SCI) filter may be realizedaccording to other alternative embodiments. For example, theinterpolating FIR circuit topology 400 depicted in FIG. 4 has been sizedfor a digital data transmission application where the maximum rate is 60M symbols/sec. Other applications could result in FIR filters withlonger or shorter apertures, different bit resolutions, samplepipelining, etc. Moreover, the direct form, FIR topology is shown,whereas other standard-form topologies could be used as well.Alternatively, interlaced sliding coefficient sets from the memory andalternating a single multiplier-accumulator could be used, but for thisexample, it would need to be eight times faster than the implementationof FIG. 4. Yet another embodiment would be a table look-up, where thefiltering convolution results are pre-computed, and a concatenatedaddress of the data and clock patterns access the memory. Thedisadvantage with the table look-up approach, however, is that memorysize grows geometrically when the incoming data levels are more thanbinary. Hence, the density required quickly becomes unrealisticallylarge.

Accordingly, example embodiments of the invention can provide thetechnical effects of creating certain systems and methods that providean ability to operate over several orders-of-magnitude in data rate witha single analog filter. Embodiments of the invention can provide thefurther technical effects of providing systems and methods for eitherbaseband or IF sampling. Embodiments of the invention may also providethe technical effects of creating certain systems and methods thatprovide simplicity and compactness of DSP element topology withcontinuous, inherent augmentations that may benefit from continuedadvances in digital memory technology. Embodiments of the invention canprovide the further technical effects of providing systems and methodsfor building amplitude and phase pre-distortion directly into the FIRcharacteristic.

Pre Averaged Staggered Convolution Decimating (PASCoDec) Filter

In accordance with example embodiments of the invention, a pre-averagedstaggered convolution decimating (PASCoDec) filter is provided. The name“multirate digital decimating filter” may be used interchangeably todenote the PASCoDec filter. The PASCoDec filter and the SCI filter(described above) share some similarities, particularly with regard tothe finite impulse (FIR) circuit topology. However, the PASCoDec filtermay be associated with a receiver portion of digital data communicationssystem, rather than with the transmitter. Embodiments of the PASCoDecfilter may provide a Nyquist bandlimiting filter. According to exampleembodiments of the invention, the PASCoDec filter may be ahardware-efficient manner for implementing a multirate digitaldecimating filter.

In accordance with example embodiments, a pre-averaging filter may beutilized to reduce the number of elements in the FIR circuit topology(e.g., multipliers, delays, and summing nodes). In an exampleembodiment, the implementation may be realized in a two-stage process tominimize hardware complexity. In the first stage, the incoming samplingrate may be decimated down to two samples per symbol. Then in the secondstage, the functions of precisely controlled bandlimiting andpre-distortion may be realized. In interfacing the resultant signal intothe analog domain, several orders-of-magnitude of continuously variablesample rate operations can typically be attained with a single analoganti-aliasing (AA) filter. The technique works equally well with eitherbaseband or intermediate frequency (IF) sampling, but with IF samplingthe maximum rate for a given hardware technology is cut in half.

In accordance with example embodiments of the invention, the PASCoDecfilter may provide a relatively rate-independent decimation functionwith minimum hardware and maximum speed. The hardware and speedimprovements may be achieved by a filter decimator block that averagesdown input samples to a manageable number. An aspect of the invention,according to certain embodiments, is that it may employ a pre-averagingfunction up front to reduce the required sample rate. Another aspect ofthe invention, according to example embodiments, is that it mayrepeatedly apply a convolution function, where filter coefficients aresuccessively computed by a relatively compact FIR circuit topology. Inthis manner, the number of digital multipliers and adds required for theFIR remains fixed, and the Nyquist shaping can be precisely controlled.Additionally, continuously variable data rate operation is achievablewith this sample decimation scheme, by increasing the number of samplesper symbol as the data rate is reduced.

Additional aspects or embodiments of the invention may include systemsand methods that may enable sampling received symbol data, whereinsampling comprises sampling in-phase or quadrature-phase symbol data.Example embodiments may include methods and systems that may enablesampling received symbol data. Example embodiments may include methodsand systems that may enable sampling modulated received symbol data. Inaccordance with example embodiments of the invention, the shifteddecimated FIR aperture impulse response coefficients may be shifted byone sample with respect to the decimated FIR aperture impulse responsecoefficients. According to example embodiments of the invention,detected output samples may comprise one sample per symbol. According toother alternative example embodiments of the invention, detected outputsamples may comprise more than one sample per symbol. In accordance withexample embodiments of the invention, received symbol data may befiltered to remove spectral replicas and/or noise. According to exampleembodiments, sampling the received symbol data at a selected sample rateprovides a sample per symbol rate of powers-of-two times three orpowers-of-two. According to example embodiments, pre-averaging threesamples per symbol to two samples per symbol comprises passing one ofthe samples to an output, and averaging the other two samples beforesending them to the output, wherein averaging comprises digitally addingthe other two symbols and bit shifting the result.

An example Nyquist bandlimiting decimating system 800 block diagram,comprising a multirate digital decimating filter, is shown in FIG. 8.The input digital data signal 806 comes in at two samples per symbol,and a set each of Nyquist-shaped detection 812 and transition 814samples go out, at a combined effective rate of two samples per symbol.The input digital data signal 806 samples as well are twice successivelyconvolved at one sample per symbol yielding alternate output samples. Inan example data demodulator application embodiment, the Nyquist-shapeddata detection 812 samples would feed a data symbol detector, as well asthe leveling control and carrier recovery circuits. Data transition 814samples would drive symbol timing recovery circuitry.

According to example embodiments, a decimating receive Nyquist filter802 may apply one or more of anti-aliasing, sampling, and pre-averagingto the incoming input digital signal 806 stream. FIR coefficients 804may then be applied to produce decimated Nyquist-shaped detection 812samples, which may be further demodulated. In accordance with exampleembodiments of the invention, the input digital data signal 806 may besampled and down converted, where the down conversion ratio may be setby the input sample rate NRs 808, 810. In certain example embodimentsthe value N may be set to 2. In other example embodiments the N can beset to any convenient required by the system design.

FIG. 9 depicts another block diagram of an example Nyquist bandlimitingdecimating system 900, comprising a multirate digital decimating filter.According to example embodiments of the invention, certain hardware maybe included for implementing the Nyquist bandlimiting decimating system900. For example, the system 900 may include a receiver 920 forreceiving input data 922. The receiver may include an anti-aliasingfilter 924, a sampling analog to digital converter 926, and apre-averaging filter/decimator 928. (The pre-averaging filter/decimatorwill be further explained with reference to FIGS. 10 and 11 below). Thereceiver may adjust the sample rate of the input data 922 based on asample rate error signal 946 to produce pre-averaged data 940 forfurther filtering with a FIR filter 932.

The Nyquist bandlimiting decimating system 900 may also include acomputer 902 having at least one memory 904 and one or more processors906. The at least one memory 904 may be accessible by the one or moreprocessors 906, and filter coefficients 916 may be stored in the one ormore memories 904. The one or more processors may be programmed,operable to, or configured for providing filter coefficients forutilization in a convolution with pre-averaged data 940 via a FIR filter932. The FIR filter 932 may include shift registers 934, multipliers936, and summing nodes 938. The FIR filter 932 may produce Nyquistbandlimited symbol data 942, which may be demultiplexed by ademultiplexer 944. According to an example embodiment, the demultiplexer944 may produce in-phase (I) decimated samples 950 and/or quadraturephase (Q) decimated samples 952. The demodulator may also detectzero-crossing samples to produce a sample rate error signal 946 foradjusting the receiver 920 sample rate. According to example embodimentsof the invention, the one or more processors 906 may be configured,programmed, or operable to perform memory 904 accesses, timing, andother functions associated with the convolution process. A particularimplementation of pre-averaging filter/decimator 928 will be discussedbelow with reference to FIGS. 10 and 11.

A block diagram of a pre-averaging filter/decimator 1000 is depicted inFIG. 10. According to example embodiments, the pre-averagingfilter/decimator 1000 reduces the hardware requirement of the PASCoDecfilter. For example, samples from an incoming signal 1002 (sampled at Nsamples per symbol) may be averaged down through one of two paths 1003,1004 depending on the number N of samples per symbol, to decimated I orQ output samples 1020 at two samples per symbol. The output may befurther processed with a precision filter, which may be pre-distorted tocompensate for the effect of averaging. According to exampleembodiments, when the number of samples per symbol is greater thanthree, an accumulator comprising a summing node 1010, a shift register1014, and an averaging loop 1016 may operate at the sample rate, and theshift register 1014 output may be sampled and reset 1012 at two samplesper symbol. According to example embodiments, the pre-averagingfilter/decimator 1000 would be bypassed if the incoming sample rate isalready at two samples per symbol.

In the case where the number of samples per symbol is three, thethree-to-two averaging path is not as straightforward. In oneembodiment, the incoming samples may be upsampled by two, prior todownsampling by three, but such an embodiment would cut the maximumoperational speed in half. According to an example embodiment of theinvention, when the number of samples per symbol is three, a fairlydirect, sample averaging approach may be accomplished via a shiftregister 1006, combining logic 1008, and a sample multiplexer 1018 toaverage down each incoming 3-tuple sample set to a uniformly time-spaced2-tuple. The process may be described with reference to FIG. 11.

FIG. 11 shows a graphical representation amplitude 1102 vs. scaled time1104 where each incoming 3-tuple sample set 1112 may be averaged down toa uniformly time-spaced 2-tuple set 1114. Although, there are countlessways to linearly interpolate incoming 3-tuple samples 1106 to yielduniformly spaced 2-tuple output samples 1108, a simple way is to passone of the input samples, and average the other two in the 3-tuplesample set 1112. The averaging may be accomplished by proportionallycombining the remaining two samples to yield an output sample thatalways falls halfway between the passed samples, or that is offset by ½sample time 1116 from 3-tuple samples 1106, as shown in FIG. 11. In thisembodiment, only a bit shift is necessary, rather than a multiplication.

According to example embodiments of the invention, pre-averaging isknown to cause a sinc (e.g., sin(πf/R_(sym))/(πf/R_(sym))) spectralaperture effect on the Nyquist channel, where R_(sym) is the symbolrate. This characteristic becomes more varied as the number of samplesin the averaging window gets smaller. FIG. 12 shows the spectralaperture effect for several averaging ratios. The spectral apertureeffect results in an aliasing effect, which can be predistorted out inthe subsequent filtering stage. For example, an inverse sinc filteraperture may be utilized to modify filter coefficients in the subsequentFIR filter processing of the signal.

TABLE 3 Baseband Sample Rates Symbol Rate Range Samples/ Sample RateRange Min (Ksps) Max (Ksps) Symbol Min (Msps) Max (Msps) 58.59 78.131536 90.00 120.00 78.13 117.19 1024 80.00 120.00 117.19 156.25 768 90.00120.00 156.25 234.38 512 80.00 120.00 234.38 312.50 384 90.00 120.00312.50 468.75 256 80.00 120.00 468.75 625.00 192 90.00 120.00 625.00937.50 128 80.00 120.00 937.50 1250.00 96 90.00 120.00 1250.00 1875.0064 80.00 120.00 1875.00 2500.00 48 90.00 120.00 2500.00 3750.00 32 80.00120.00 3750.00 5000.00 24 90.00 120.00 5000.00 7500.00 16 80.00 120.007500.00 10000.00 12 90.00 120.00 10000.00 15000.00 8 80.00 120.0015000.00 20000.00 6 90.00 120.00 20000.00 30000.00 4 80.00 120.0030000.00 40000.00 3 90.00 120.00 40000.00 60000.00 2 80.00 120.00

According to example embodiments, continuously variable rate operationmay be achieved by gear shifting the number of samples per symbol. TABLE3 above lists sample rates and ranges for continuously variable rateoperation with baseband gear shifting for a pre-averaged staggeredconvolution decimating (PASCoDec) filter, according to an exampleembodiment of the invention. The sample rate may be kept in a fixedrange, such that only a single anti aliasing (AA) filter is necessary.For purposes of illustration, a maximum data rate of 60 M symbols/sechas been arbitrarily set. In TABLE 3, note that each octave in datasymbol rate is broken up into two ratio regions, 1:1.5 and 1:1.33, wherethe upper range always has samples per symbol that are powers-of-two,and the lower range has samples per symbol that are powers-of-two times3. Also, observe that the sample rates always fall within a 1:1.5 range.Hence, in a motor vehicle analogy, the sample rate is analogous toengine RPM, the number of samples per symbol to the gear ratio, and thedata symbol rate to actual vehicle speed. The lowest integer power wouldbe two samples per symbol, for this type of modem application usingbaseband Nyquist sampling.

TABLE 4 below lists sample rates and ranges for continuously variablerate operation with intermediate frequency (IF) gear shifting for apre-averaged staggered convolution decimating (PASCoDec) filter,according to an example embodiment of the invention. For the case ofintermediate frequency (IF) sampling, the minimum number of samples persymbol is double what it is for baseband sampling. Hence, the maximumdata rate is halved. This doubling is a direct result of it being moredifficult to avoid aliasing with IF sampling. However, continuouslyvariable rate operation is still achievable, but for a given hardwaretechnology, the maximum data rate of operation is halved. IF samplinghas other advantages in that it uses less hardware than basebandsampling, and the quadrature amplitude and phase balance is automaticand precise.

TABLE 4 IF Sample Rates Symbol Rate Range Samples/ Sample Rate Range Min(Ksps) Max (Ksps) Symbol Min (Msps) Max (Msps) 29.30 39.06 3072 90.00120.00 39.06 58.59 2048 80.00 120.00 58.59 78.13 1536 90.00 120.00 78.13117.19 1024 80.00 120.00 117.19 156.25 768 90.00 120.00 156.25 234.38512 80.00 120.00 234.38 312.50 384 90.00 120.00 312.50 468.75 256 80.00120.00 468.75 625.00 192 90.00 120.00 625.00 937.50 128 80.00 120.00937.50 1250.00 96 90.00 120.00 1250.00 1875.00 64 80.00 120.00 1875.002500.00 48 90.00 120.00 2500.00 3750.00 32 80.00 120.00 3750.00 5000.0024 90.00 120.00 5000.00 7500.00 16 80.00 120.00 7500.00 10000.00 1290.00 120.00 10000.00 15000.00 8 80.00 120.00 15000.00 20000.00 6 90.00120.00 20000.00 30000.00 4 80.00 120.00

A pictorial example 1300 of the sliding convolution interpolating (SCI)filter, as applied to a Nyquist bandlimiting application, is shown inFIG. 13. This figure shows sample amplitudes 1301 vs. sample scaled time1302 for continuously clocked samples 1303. According to exampleembodiments of the invention, incoming bandlimited signal (plus noise)1304 representing N samples per symbol may be clocked, for example, froma pre-averaging decimator into a decimating receive Nyquist filter 802,as was shown in FIG. 8. In this pictorial example 1300, the incomingbandlimited signal (plus noise) 1304 represents two samples per symbol.According to example embodiments, a decimated spectral shaping impulseresponse sample set 1306 having a finite FIR aperture comprisingdecimated finite impulse response (FIR) aperture impulse responsecoefficients 1316, may be convolved with the incoming bandlimited signal(plus noise) 1304 to produce decimated signal and noise output detectionsamples 1310 (e.g., detected output samples). In example embodiments ofthe invention, the decimated spectral shaping impulse response sampleset 1306 (FIR filter waveform samples) may be selected from any numberof FIR filter impulse responses. In an example embodiment, the decimatedspectral shaping impulse response sample set 1306 (FIR filter waveformsamples) may be modeled from a “raised cosine” impulse response, whichis one of the most well-known filtering functions of the Nyquist filterfunction family. Then, a decimated staggered spectral shaping impulseresponse sample set 1308 having a finite FIR aperture comprisingdecimated finite impulse response (FIR) aperture impulse responsecoefficients 1316 may be convolved with the incoming bandlimited signal(plus noise) 1304 to produce decimated signal and noise outputtransition samples 1312 (e.g., zero-crossing transition samples).According to example embodiments of the invention, the decimated signaland noise output transition samples 1312 may represent zero crossings ofthe symbol data, and therefore, may be used in timing the sampling rateof the SCI system, for example, by providing a running average of thedecimated signal and noise output transition samples 1312 for input tothe sampling rate controller, as was shown in FIG. 9 with regard to thesample rate error signal 946.

According to an example embodiment of the invention, a generalized blockdiagram of an interpolating FIR circuit topology 1400 is shown in FIG.14. In this example embodiment, a FIR coefficient memory 1401 may beutilized to store and access FIR coefficients. The topology 1400 mayinclude a plurality of shift registers 1404, multipliers 1412, andsummation blocks 1416. In an example embodiment, an input sample stream1402, which may comprise I or Q data plus noise, and may be continuouslyclocked through the shift registers 1404. Then, after each shifting, thesample 1408 at the input and the successively shifted samples 1406 maybe multiplied via multipliers 1412 with FIR coefficients 1410. Theresulting samples may then be successively summed by summing nodes 1414,resulting in output filtered bandlimited data 1416. The output filteredbandlimited data 1416 may then be further processed by a demultiplexer1418 to produce detection I or Q decimated samples out 1420 and zerocrossing I or Q decimated samples out 1422.

Example values for the various elements of the interpolating FIR circuittopology 1400 may include: aperture widths=eight symbol times (depictedby the number of shift registers T 1404); 8×8-bit digital multipliers1412; data symbol rate range operable to vary over threeorders-of-magnitude; data sample rate range about half an octave; filtercoefficient memory 1401 size approximately equal to the maximum numberof samples per symbol times the number of symbols in aperture times thenumber of bits per sample. Hence, as is apparent from FIG. 14, theperformance burden is on the memory size and speed to keep theimplementation compact and flexible.

FIG. 15 depicts a frequency-domain representation of an anti aliasing(AA) filtering and gear shifting technique 1500 for baseband samplingand for the case where the data rate is continuously varied, accordingto example embodiments of the invention. FIG. 15 depicts demodulatedspectra amplitude 1502 vs. scaled frequency 1504. FIG. 15 also depictsexample baseband spectra 1514 and replicas due to sampling 1516.According to example embodiments, the AA (replication removal) filter1518 may be situated to remove unwanted spectral content, includingnoise 1517, or replicas due to sampling 1516. In an example embodiment,the AA (replication removal) filter 1518 may comprise an elliptic analogfilter function with an equiripple bandwidth on the order of ¾ themaximum data symbol rate, and with a passband-to-stopband shape-factoron the order of 1.15. The figure depicts spectral filtering conditionsin the highest octave of operation at the maximum symbol rate at twosamples/symbol 1506, minimum symbol rate at two samples/symbol 1508,maximum symbol rate at three samples/symbol 1510, and minimum symbolrate at three samples/symbol 1512. Accordingly, subsequent octaves mayoccupy less bandwidth and may be progressively less affected by theanti-aliasing filter 1518 characteristics. In certain gear-shiftingsettings, the noise floor 1517 may be aliased 1522. In these situations,additional filtering may be applied, according to example embodiments,to further reduce any noise that is passed.

FIG. 16 depicts a frequency-domain representation of an anti-aliasing(AA) filtering and gear-shifting technique 1600 (which is analogous tothe baseband case) for IF sampling in the first Nyquist zone, and forthe case where the data rate is continuously varied, according toexample embodiments of the invention. FIG. 16 depicts demodulatedspectra amplitude 1602 vs. scaled frequency 1604. FIG. 16 also depictsexample IF spectra 1614 and replicas due to sampling 1616. According toexample embodiments, the AA (replication removal) filter 1618 may besituated to remove unwanted spectral content, including noise 1617, orreplicas due to sampling 1616. In an example embodiment, the AA(replication removal) filter 1618 may comprise an elliptic analog filterfunction with an equiripple bandwidth on the order of 3/2 the maximumdata symbol rate, and with a passband-to-stopband shape-factor on theorder of 1.15. The figure depicts spectral filtering conditions in thehighest octave of operation at the maximum symbol rate at 4samples/symbol 1606, minimum symbol rate at 4 samples/symbol 1608,maximum symbol rate at 6 samples/symbol 1610, and minimum symbol rate at6 samples/symbol 1612. Accordingly, subsequent octaves may occupy lessbandwidth and may be progressively less affected by the AA filter 1618characteristics. In certain gear-shifting settings, the noise 1617 maybe aliased 1622. In these situations, additional filtering may beapplied, according to example embodiments, to further reduce any noisethat is passed.

According to example embodiments of the invention, the spectraloccupancy at the highest data rate in the first octave of operation maybe broad enough that the lowpass elliptic AA filter used in the basebandfilter may also be applicable to the IF filter, allowing theimplementation to be digitally-switched from lowpass to bandpasssampling, without changing the AA filter 1618.

An example method 1700 for implementing a multirate digital decimatingfilter (e.g., the pre-averaged staggered convolution decimating(PASCoDec) filter) will now be described with reference to the flowdiagram of FIG. 17. In block 1702 and according to an example embodimentof the invention, the method may include sampling the received symboldata at a selected sample rate. In block 1704, the received sampledsymbol data is pre-averaged to provide two samples per symbol. In block1706, the pre-averaged samples are convolved with the decimated FIRaperture impulse response coefficients to produce detected outputsamples. In block 1708, the pre-averaged samples are convolved withshifted decimated FIR aperture impulse response coefficients to producezero-crossing transition samples. In block 1710, the sample rate isadjusted based at least in part on averaging the zero-crossingtransition samples.

The embodiments depicted in the tables and figures herein are sized fora digital data transmission application where the maximum rate is 60 Msymbols/sec. Other applications could result in FIR filters with longeror shorter apertures, different bit resolutions, different samplepipelining, etc. Moreover, the direct form, FIR topology is shown inFIG. 14, whereas other standard-form topologies could be used, inaccordance with alternate embodiments of the invention. A beneficialaspect of the invention is the use of a pre-averager in conjunction withrepeated application of filter coefficients. Alternately, a singlemultiplier-accumulator could be used; but for this example, it wouldneed to be eight times faster than the implementation of FIG. 14. Atable look-up approach, where the filtering convolution results arepre-computed, could also be utilized; however, such an approachtypically is not practical when the input data contains noise.

Accordingly, example embodiments of the invention can provide thetechnical effects of creating certain systems and methods forimplementing a pre-averaged staggered convolution decimating filter.Embodiments of the invention can provide the further technical effectsof providing systems and methods for operating the filter over severalorders of magnitude in data rate with a single analog filter.Embodiments of the invention may also provide the technical effects ofcreating certain systems and methods that provide operating the filterfor either baseband or IF sampling. Embodiments of the invention canprovide the further technical effects of providing systems and methodsfor a simple compact filtering digital signal processing (DSP) elementtopology with continuous, inherent augmentation ability as the digitalaccumulator and memory technology is advanced. Embodiments of theinvention can also provide systems and methods for filtering whereamplitude and phase pre-distortion may be directly built into the FIRcharacteristics.

In example embodiments of the invention, the Nyquist bandlimitinginterpolation system 100, 200 and the Nyquist bandlimiting decimatingsystem 800, 900 may include any number of software applications that areexecuted to facilitate any of the operations.

In example embodiments, one or more input/output interfaces mayfacilitate communication between the Nyquist bandlimiting interpolationsystem 100, 200 or the Nyquist bandlimiting decimating system 800, 900,and one or more input/output devices. For example, a universal serialbus port, a serial port, a disk drive, a CD-ROM drive, and/or one ormore user interface devices, such as a display, keyboard, keypad, mouse,control panel, touch screen display, microphone, etc., may facilitateuser interaction with the Nyquist bandlimiting interpolation system 100,200 or the Nyquist bandlimiting decimating system 800, 900. The one ormore input/output interfaces may be utilized to receive or collect dataand/or user instructions from a wide variety of input devices. Receiveddata may be processed by one or more computer processors as desired invarious embodiments of the invention and/or stored in one or more memorydevices.

One or more network interfaces may facilitate connection of the Nyquistbandlimiting interpolation system 100, 200 or the Nyquist bandlimitingdecimating system 800, 900 inputs and outputs to one or more suitablenetworks and/or connections; for example, the connections thatfacilitate communication with any number of sensors associated with thesystem. The one or more network interfaces may further facilitateconnection to one or more suitable networks; for example, a local areanetwork, a wide area network, the Internet, a cellular network, a radiofrequency network, a Bluetooth™ enabled network, a Wi-Fi™ enablednetwork, a satellite-based network, any wired network, any wirelessnetwork, etc., for communication with external devices and/or systems.

As desired, embodiments of the invention may include the Nyquistbandlimiting interpolation system 100, 200 and/or the Nyquistbandlimiting decimating system 800, 900 with more or less of thecomponents illustrated in any of these figures herein.

The invention is described above with reference to block and flowdiagrams of systems, methods, apparatuses, and/or computer programproducts according to example embodiments of the invention. It will beunderstood that one or more blocks of the block diagrams and flowdiagrams, and combinations of blocks in the block diagrams and flowdiagrams, respectively, can be implemented by computer-executableprogram instructions. Likewise, some blocks of the block diagrams andflow diagrams may not necessarily need to be performed in the orderpresented, or may not necessarily need to be performed at all, accordingto some embodiments of the invention.

These computer-executable program instructions may be loaded onto ageneral-purpose computer, a special-purpose computer, a processor, orother programmable data processing apparatus to produce a particularmachine, such that the instructions that execute on the computer,processor, or other programmable data processing apparatus create meansfor implementing one or more functions specified in the flow diagramblock or blocks. These computer program instructions may also be storedin a computer-readable memory that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory produce an article of manufacture including instruction meansthat implement one or more functions specified in the flow diagram blockor blocks. As an example, embodiments of the invention may provide for acomputer program product, comprising a computer-usable medium having acomputer-readable program code or program instructions embodied therein,said computer-readable program code adapted to be executed to implementone or more functions specified in the flow diagram block or blocks. Thecomputer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational elements or steps to be performed on the computer or otherprogrammable apparatus to produce a computer-implemented process suchthat the instructions that execute on the computer or other programmableapparatus provide elements or steps for implementing the functionsspecified in the flow diagram block or blocks.

Accordingly, blocks of the block diagrams and flow diagrams supportcombinations of means for performing the specified functions,combinations of elements or steps for performing the specified functionsand program instruction means for performing the specified functions. Itwill also be understood that each block of the block diagrams and flowdiagrams, and combinations of blocks in the block diagrams and flowdiagrams, can be implemented by special-purpose, hardware-based computersystems that perform the specified functions, elements or steps, orcombinations of special-purpose hardware and computer instructions.

While the invention has been described in connection with what ispresently considered to be the most practical and various embodiments,it is to be understood that the invention is not to be limited to thedisclosed embodiments, but on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the scope ofthe appended claims. Although specific terms are employed herein, theyare used in a generic and descriptive sense only and not for purposes oflimitation.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined in the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal language of the claims.

The claimed invention is:
 1. A method for implementing a multiratedigital decimating filter for filtering received symbol data comprising:sampling the received symbol data at a selected sample rate;pre-averaging the sampled received symbol data from three samples persymbol to two samples per symbol by passing one of the three samples toan output, and averaging the other two samples before sending them tothe output, wherein the averaging comprises digitally adding the othertwo samples and bit shifting the result; convolving the pre-averagedsamples with decimated finite impulse response (FIR) aperture impulseresponse coefficients; generating, based at least in part on convolvingthe pre-averaged samples, decimated in-phase (I) output samples anddecimated quadrature-phase (Q) output samples; convolving thepre-averaged samples with shifted decimated FIR aperture impulseresponse coefficients to produce zero-crossing transition samples; andadjusting the sample rate based at least in part on averaging thezero-crossing transition samples.
 2. The method of claim 1, whereinsampling the received symbol data comprises sampling in-phase orquadrature-phase symbol data.
 3. The method of claim 1, wherein theshifted decimated FIR aperture impulse response coefficients are shiftedby one sample with respect to the decimated FIR aperture impulseresponse coefficients.
 4. The method of claim 1, wherein the decimated Ioutput samples and decimated Q output samples comprise one sample persymbol, respectively.
 5. The method of claim 1, further comprisingfiltering the received symbol data to remove spectral replicas.
 6. Themethod of claim 1, wherein sampling the received symbol data at aselected sample rate provides a sample per symbol rate of powers-of-twotimes three or powers-of-two.
 7. A system for implementing a multiratedigital decimating filter for filtering received symbol data, the systemcomprising: a receiver for receiving symbol data; at least one memoryfor storing data and computer-executable instructions; at least oneprocessor configured to access the at least one memory and furtherconfigured to execute the computer-executable instructions to: samplethe received symbol data at a selected sample rate; pre-average thesampled received data from three samples per symbol to two samples persymbol by passing one of the three samples to an output, and averagingthe other two samples before sending them to the output, wherein theaveraging comprises digitally adding the other two samples and bitshifting the result; convolve the pre-averaged samples with decimatedFIR aperture impulse response coefficients; generate, based at least onthe convolved pre-averaged samples, decimated in-phase (I) outputsamples and decimated quadrature-phase (Q) output samples; convolve thepre-averaged samples with shifted decimated FIR aperture impulseresponse coefficients to produce decimated detected zero-crossingtransition samples; and adjust the sample rate based at least in part onaveraging the zero-crossing transition samples.
 8. The system of claim7, wherein the at least one processor is further configured to samplethe received symbol data comprising in-phase or quadrature-phase symboldata.
 9. The system of claim 7, wherein the shifted decimated FIRaperture impulse response coefficients are shifted by one sample withrespect to the decimated FIR aperture impulse response coefficients. 10.The system of claim 7, further comprising an anti-aliasing filter toremove spectral replicas from the sampled received symbol data.
 11. Thesystem of claim 7, wherein the decimated I output samples and thedecimated Q output samples comprise one sample per symbol, respectively.12. The system of claim 7, wherein the data comprises digital symbols.13. The system of claim 7, wherein the at least one processor is furtherconfigured to sample the received symbol data at a sample per symbolrate of powers-of-two times three or powers-of-two.
 14. A filter fordemodulating and filtering received symbol data, the filter comprising:at least one memory device for storing data and computer-executableinstructions; at least one processor configured to access the at leastone memory and further configured to execute the computer-executableinstructions to: sample the received symbol data at a selected samplerate; filter the sampled received symbol data to remove spectralreplicas; pre-average the sampled received data from three samples persymbol to two samples per symbol by passing one of the three samples toan output, and averaging the other two samples before sending them tothe output, wherein the averaging comprises digitally adding the othertwo samples and bit shifting the result; convolve the pre-averagedsamples with decimated FIR aperture impulse response coefficients;generate, based at least on the convolved pre-averaged samples,decimated in-phase (I) output samples and decimated quadrature-phase (Q)output samples; convolve the pre-averaged samples with shifted decimatedFIR aperture impulse response coefficients to produce decimated detectedzero-crossing transition samples; and adjust the sample rate based atleast in part on averaging the zero-crossing transition samples.
 15. Thefilter of claim 14, wherein the at least one processor is furtherconfigured to accumulate the decimated I output samples, the decimated Qoutput samples, and the decimated zero-crossing transition samples. 16.The filter of claim 14, wherein the at least one processor is furtherconfigured to demultiplex the accumulated samples.
 17. The filter ofclaim 14, wherein the shifted decimated FIR aperture impulse responsecoefficients are shifted by one sample with respect to the decimated FIRaperture impulse response coefficients.
 18. The filter of claim 14,wherein the at least one processor is further configured to sample thereceived symbol data at a sample per symbol rate of powers-of-two timesthree or powers-of-two.